A362848 a(n) = Sum_{k=0..n} 4^k * Gamma(n + k + 1/2) / Gamma(n - k + 1/2). Row sums of A362847.

1, 4, 121, 11376, 2165689, 689873284, 330204013569, 221470234531456, 198160750081637521, 228040136335670652324, 328106086348844570538409, 577082259304437657893671984, 1218130815379359944856599793801, 3039062974890293661892991548863076

Offset: 0

Author

Peter Luschny, May 05 2023

Keywords

• nonn

Crossrefs

Cf. A362847.

Programs

Mathematica

a[n_]:= Sum[(2*(n+k)-1)!!/(2*(n-k)-1)!!,{k,0,n}];Flatten[Table[a[n],{n,0,13}]] (* Detlef Meya, Oct 09 2023 *)

Formula

a(n) = Sum_{k=0..n} (2*(n + k) - 1)!! / (2*(n - k) - 1)!!. - Detlef Meya, Oct 09 2023

a(n) ~ 2^(4*n + 1/2) * n^(2*n) / exp(2*n). - Vaclav Kotesovec, Oct 09 2023